On Z(4)-linear Goethals codes and Kloosterman sums

Authors
Helleseth, T Zinoviev, V
Citation
T. Helleseth et V. Zinoviev, On Z(4)-linear Goethals codes and Kloosterman sums, DES CODES C, 17(1-3), 1999, pp. 269-288
Citations number
13
Categorie Soggetti
Computer Science & Engineering
Journal title
DESIGNS CODES AND CRYPTOGRAPHY
ISSN journal
09251022 → ACNP
Volume
17
Issue
1-3
Year of publication
1999
Pages
269 - 288
Database
ISI
SICI code
0925-1022(199909)17:1-3<269:OZGCAK>2.0.ZU;2-Z
Abstract
Studying the coset weight distributions of the Z(4)-linear Goethals codes, e connect these codes with the Kloosterman sums. From one side, we obtain f or some cases, of the cosets of weight four, the exact expressions for the number of code ords of weight four in terms of the Kloosterman sums. From t he other side, we obtain some limitations for the possible values of the Kl oosterman sums, which improve the well known results due to Lachaud and Wol fmann [11].